Research in Integrable Quantum Field Theory

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

This award funds the research activities of Professor Sergei Lukyanov at Rutgers, The State University of New Jersey. Since its inception in the 1920's, Quantum Field Theory (QFT) has become an indispensable tool in modern theoretical physics. Apart from particle physics --- the original motivation for developing this framework --- it has found remarkable success in describing the physics of phase transitions as well as numerous applications in many-body systems, turbulence, cosmology, etc. As the list of topics continues to expand, we are forced to constantly revise our fundamental understanding of QFT and incorporate new powerful mathematical techniques that can handle problems of increasing complexity. A perfect theoretical laboratory for doing this has turned out to involve low-dimensional "integrable" models and conformal field theories. These are theories that possess a large, oftentimes infinite, set of symmetries that together allow the use of powerful exact methods for their solution. In turn this elevated degree of control has led --- and is still leading --- to profound insights into many important physical concepts. As a result, the field of Integrable Quantum Field Theory (IQFT) sits at the cutting edge of theoretical high-energy physics. The research of Professor Lukyanov is aimed at the further development of IQFTs. A successful realization would allow one to overcome the notorious technical difficulties that emerge when traditional methods are applied to many of the theories that appear within the context of mainstream theoretical high-energy physics. This research is therefore in the national interest because it will have an important impact on the development and understanding of fundamental science within the United States. Professor Lukyanov also intends to involve graduate students and postdocs in his research and disseminate the results to the broader community of young scientists via lectures and workshops. More technically, this research is focused on integrable quantum spin chains and non-linear sigma models --- exactly the types of theories that emerge within the context of gauge/string duality. This research is organized into three projects. The first is the study of a certain multiparametric quantum spin chain at criticality. The key to the approach will be the so-called ODE/IQFT correspondence, a new mathematical tool of Integrable Quantum Field Theories ("IQFT" side) which allows one to "encode" its algebraic structures into a system of Ordinary Differential Equations ("ODE" side). This part is directly related to the gauge/string duality. The second project is devoted to the study of the high-energy asymptotics of scattering amplitudes in quantum chromodynamics. The ultimate objective of the third project is to extend the ODE/IQFT approach to integrable non-linear sigma models. The new methods considered in this project, when fully developed, should be of broad impact. The first and third projects could lead to entirely new directions and discoveries, including potential applications to the description of disordered systems in condensed-matter physics. By contrast, the second project has to do with a realistic problem in particle physics. All three projects provide excellent training opportunities for students in QFT and statistical mechanics, from undergraduate-level problems to advanced training in the most abstract analytic techniques. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.